Question: make a stem leaf graph with two 4s, two 5, etc. 41 43 46 46 47 48 49 49 50 50 51 51 51 51 52 52 54 54 54 54 54 55 55 55 55 56 56 56 57 57 57 57 59 60 61 61 61 62 64 64 65 67 69
1. **State the problem:**
We need to create a stem-and-leaf plot for the given data set:
$$41, 43, 46, 46, 47, 48, 49, 49, 50, 50, 51, 51, 51, 51, 52, 52, 54, 54, 54, 54, 54, 55, 55, 55, 55, 56, 56, 56, 57, 57, 57, 57, 59, 60, 61, 61, 61, 62, 64, 64, 65, 67, 69$$
2. **Explain the stem-and-leaf plot:**
- The "stem" represents the leading digit(s) of each number.
- The "leaf" represents the last digit of each number.
- Each stem row lists all leaves corresponding to that stem.
3. **Organize the data by stems:**
- Stems are the tens digits: 4, 5, 6
- Leaves are the units digits.
4. **List leaves for each stem:**
- Stem 4: Leaves are $$1, 3, 6, 6, 7, 8, 9, 9$$
- Stem 5: Leaves are $$0, 0, 1, 1, 1, 1, 2, 2, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 9$$
- Stem 6: Leaves are $$0, 1, 1, 1, 2, 4, 4, 5, 7, 9$$
5. **Write the stem-and-leaf plot:**
$$\begin{array}{c|l}
\text{Stem} & \text{Leaves} \\
\hline
4 & 1\ 3\ 6\ 6\ 7\ 8\ 9\ 9 \\
5 & 0\ 0\ 1\ 1\ 1\ 1\ 2\ 2\ 4\ 4\ 4\ 4\ 4\ 5\ 5\ 5\ 5\ 6\ 6\ 6\ 7\ 7\ 7\ 7\ 9 \\
6 & 0\ 1\ 1\ 1\ 2\ 4\ 4\ 5\ 7\ 9
\end{array}$$
6. **Interpretation:**
- Each number in the data set is represented by a stem and a leaf.
- For example, $$46$$ is stem $$4$$ and leaf $$6$$.
- The plot shows the distribution of the data clearly.
**Final stem-and-leaf plot:**
$$\begin{array}{c|l}
4 & 1\ 3\ 6\ 6\ 7\ 8\ 9\ 9 \\
5 & 0\ 0\ 1\ 1\ 1\ 1\ 2\ 2\ 4\ 4\ 4\ 4\ 4\ 5\ 5\ 5\ 5\ 6\ 6\ 6\ 7\ 7\ 7\ 7\ 9 \\
6 & 0\ 1\ 1\ 1\ 2\ 4\ 4\ 5\ 7\ 9
\end{array}$$